Thanks for the question. @swolny and others can correct me here, but I think a good approach to considering contributions from each LULC class to the water yield volume in a given watershed is to create scenarios.
If we were interested in knowing how agriculture vs development vs conservation (forests perhaps) impacted water yield volume, we might run the model first with agriculture LULC values and then change those values or a subset of those values to developed. Running the model again we could compare the difference in output. We could then do the same thing for our conservation scenario. I think that these kinds of watershed / sub-watershed comparisons are what the model was designed for; getting a sense of how different landscape practices might effect annual water yield outcomes.
Unlike our other water models (Seasonal Water Yield, SDR, NDR), Annual Water Yield does not do any routing of surface water. Because of this, I suppose looking at the pixel output would tell you the straight up difference between LULC types since there are no interactions between them. It would be the same as using the equations in the Users Guide to compare. HOWEVER, I believe the equations used were designed for the watershed / sub-watershed level, so use those values relatively and not as absolute truths.
Hopefully that was more helpful then confusing!